ESD: Compute the empirical spectral distribution (ESD) for a set of population
eigenvalues
Description
The Marcenko Pastur (MP) law relates the limiting distribution
of the sample eigenvalues to that of the population eigenvalues. In the
finite-dimensional case, the population spectral distribution (PSD) can be
represented as a sum of point masses, and the empirical spectral
distribution (ESD) can be obtained by solving the discretized MP equation.
Theoretical and implementation details in the references.
Usage
ESD(tau, n)
Arguments
tau
(Required) A non-negative numeric vector of population
eigenvalues.
n
(Required) A positive integer representing the number of datapoints
of a hypothetical data matrix with dimension c(n, p = length(tau)).
Value
A named numeric vector of containing points of the ESD. The names
give the corresponding points on the x axis.
References
Ledoit, O. and Wolf, M. (2015). Spectrum
estimation: a unified framework for covariance matrix estimation and PCA in
large dimensions. Journal of Multivariate Analysis, 139(2)
Ledoit, O.
and Wolf, M. (2016). Numerical Implementation of the QuEST function.
arXiv:1601.05870 [stat.CO]